mirror of https://github.com/CGAL/cgal
de-math:
perl -p -i -e 's/\\f\$\s([a-w])\\f\$/`$1`/g' *.h
This commit is contained in:
Sébastien Loriot
parent
4905c23e75
commit
c4e40f96c3
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@ -94,14 +94,14 @@ introduces an identity transformation.
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Aff_transformation_2(const Identity_transformation& );
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/*!
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introduces a translation by a vector \f$ v\f$.
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introduces a translation by a vector `v`.
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*/
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Aff_transformation_2(const Translation,
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const Vector_2<Kernel> &v);
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/*!
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approximates the rotation over the angle indicated by direction
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\f$ d\f$, such that the differences between the sines and cosines
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`d`, such that the differences between the sines and cosines
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of the rotation given by d and the approximating rotation
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are at most \f$ num/den\f$ each.
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\pre \f$ num/den>0\f$ and \f$ d != 0\f$.
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@ -50,7 +50,7 @@ introduces an identity transformation.
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Aff_transformation_3(const Identity_transformation& );
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/*!
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introduces a translation by a vector \f$ v\f$.
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introduces a translation by a vector `v`.
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*/
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Aff_transformation_3(const Translation,
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const Vector_3<Kernel> &v);
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@ -25,22 +25,22 @@ public:
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/// @{
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/*!
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introduces the direction `d` of vector \f$ v\f$.
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introduces the direction `d` of vector `v`.
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*/
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Direction_2(const Vector_2<Kernel> &v);
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/*!
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introduces the direction `d` of line \f$ l\f$.
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introduces the direction `d` of line `l`.
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*/
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Direction_2(const Line_2<Kernel> &l);
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/*!
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introduces the direction `d` of ray \f$ r\f$.
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introduces the direction `d` of ray `r`.
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*/
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Direction_2(const Ray_2<Kernel> &r);
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/*!
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introduces the direction `d` of segment \f$ s\f$.
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introduces the direction `d` of segment `s`.
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*/
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Direction_2(const Segment_2<Kernel> &s);
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@ -131,7 +131,7 @@ returns a vector that has the same direction as `d`.
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Vector_2<Kernel> vector() const;
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/*!
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returns the direction obtained by applying \f$ t\f$ on `d`.
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returns the direction obtained by applying `t` on `d`.
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*/
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Direction_2<Kernel> transform(const Aff_transformation_2<Kernel> &t) const;
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@ -25,22 +25,22 @@ public:
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/*!
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introduces a direction `d` initialized with the
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direction of vector \f$ v\f$.
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direction of vector `v`.
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*/
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Direction_3(const Vector_3<Kernel> &v);
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/*!
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introduces the direction `d` of line \f$ l\f$.
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introduces the direction `d` of line `l`.
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*/
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Direction_3(const Line_3<Kernel> &l);
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/*!
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introduces the direction `d` of ray \f$ r\f$.
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introduces the direction `d` of ray `r`.
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*/
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Direction_3(const Ray_3<Kernel> &r);
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/*!
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introduces the direction `d` of segment \f$ s\f$.
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introduces the direction `d` of segment `s`.
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*/
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Direction_3(const Segment_3<Kernel> &s);
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@ -97,7 +97,7 @@ returns a vector that has the same direction as `d`.
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Vector_3<Kernel> vector() const;
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/*!
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returns the direction obtained by applying \f$ t\f$ on `d`.
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returns the direction obtained by applying `t` on `d`.
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*/
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Direction_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;
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@ -28,7 +28,7 @@ public:
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/*!
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introduces an iso-oriented cuboid `c` with diagonal
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opposite vertices \f$ p\f$ and \f$ q\f$. Note that the object is
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opposite vertices `p` and `q`. Note that the object is
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brought in the canonical form.
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*/
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Iso_cuboid_3(const Point_3<Kernel> &p,
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@ -36,7 +36,7 @@ const Point_3<Kernel> &q);
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/*!
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introduces an iso-oriented cuboid `c` with diagonal
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opposite vertices \f$ p\f$ and \f$ q\f$. The `int` argument value
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opposite vertices `p` and `q`. The `int` argument value
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is only used to distinguish the two overloaded functions.
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\pre \f$ p.x()<=q.x()\f$, \f$ p.y()<=q.y()\f$ and \f$ p.z()<=q.z()\f$.
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*/
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@ -146,14 +146,14 @@ returns largest %Cartesian
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Kernel::FT zmax() const;
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/*!
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returns \f$ i\f$-th %Cartesian coordinate of
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returns `i`-th %Cartesian coordinate of
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the smallest vertex of `c`.
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\pre \f$ 0 \leq i \leq2\f$.
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*/
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Kernel::FT min_coord(int i) const;
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/*!
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returns \f$ i\f$-th %Cartesian coordinate of
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returns `i`-th %Cartesian coordinate of
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the largest vertex of `c`.
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\pre \f$ 0 \leq i \leq2\f$.
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*/
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@ -174,7 +174,7 @@ bool is_degenerate() const;
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returns either \ref ON_UNBOUNDED_SIDE,
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\ref ON_BOUNDED_SIDE, or the constant
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\ref ON_BOUNDARY,
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depending on where point \f$ p\f$ is.
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depending on where point `p` is.
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*/
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Bounded_side bounded_side(const Point_3<Kernel> &p) const;
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@ -209,7 +209,7 @@ returns a bounding box containing `c`.
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Bbox_3 bbox() const;
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/*!
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returns the iso-oriented cuboid obtained by applying \f$ t\f$ on
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returns the iso-oriented cuboid obtained by applying `t` on
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the smallest and the largest of `c`.
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\pre The angle at a rotation must be a multiple of \f$ \pi/2\f$, otherwise the resulting cuboid does not have the same size. Note that rotating about an arbitrary angle can even result in a degenerate iso-oriented cuboid.
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*/
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@ -29,7 +29,7 @@ public:
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/*!
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introduces an iso-oriented rectangle `r` with diagonal
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opposite vertices \f$ p\f$ and \f$ q\f$. Note that the object is
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opposite vertices `p` and `q`. Note that the object is
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brought in the canonical form.
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*/
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Iso_rectangle_2(const Point_2<Kernel> &p,
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@ -37,7 +37,7 @@ const Point_2<Kernel> &q);
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/*!
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introduces an iso-oriented rectangle `r` with diagonal
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opposite vertices \f$ p\f$ and \f$ q\f$. The `int` argument value
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opposite vertices `p` and `q`. The `int` argument value
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is only used to distinguish the two overloaded functions.
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\pre \f$ p.x()<=q.x()\f$ and \f$ p.y()<=q.y()\f$.
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*/
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@ -125,14 +125,14 @@ returns the \f$ y\f$ coordinate of upper right vertex of `r`.
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Kernel::FT ymax() const;
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/*!
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returns the \f$ i\f$'th %Cartesian coordinate of the
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returns the `i`'th %Cartesian coordinate of the
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lower left vertex of `r`.
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\pre \f$ 0 \leq i \leq1\f$.
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*/
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Kernel::FT min_coord(int i) const;
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/*!
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returns the \f$ i\f$'th %Cartesian coordinate of the
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returns the `i`'th %Cartesian coordinate of the
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upper right vertex of `r`.
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\pre \f$ 0 \leq i \leq1\f$.
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*/
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@ -153,7 +153,7 @@ bool is_degenerate() const;
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returns either \ref ON_UNBOUNDED_SIDE,
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\ref ON_BOUNDED_SIDE, or the constant
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\ref ON_BOUNDARY,
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depending on where point \f$ p\f$ is.
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depending on where point `p` is.
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*/
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Bounded_side bounded_side(const Point_2<Kernel> &p) const;
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@ -188,7 +188,7 @@ returns a bounding box containing `r`.
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Bbox bbox() const;
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/*!
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returns the iso-oriented rectangle obtained by applying \f$ t\f$ on
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returns the iso-oriented rectangle obtained by applying `t` on
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the lower left and the upper right corner of `r`.
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\pre The angle at a rotation must be a multiple of \f$ \pi/2\f$, otherwise the resulting rectangle does not have the same side length. Note that rotating about an arbitrary angle can even result in a degenerate iso-oriented rectangle.
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*/
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@ -12,11 +12,11 @@ If this type does not exist, a specialization of `Kernel_traits` can be
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used to provide the desired information.
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This class is, for example, useful in the following context. Assume
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you want to write a generic function that accepts two points \f$ p\f$ and
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\f$ q\f$ as argument and constructs the line segment between \f$ p\f$ and \f$ q\f$.
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you want to write a generic function that accepts two points `p` and
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`q` as argument and constructs the line segment between `p` and `q`.
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In order to specify the return type of this function, you need to know
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what is the segment type corresponding to the Point type representing
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\f$ p\f$ and \f$ q\f$. Using `Kernel_traits`, this can be done as follows.
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`p` and `q`. Using `Kernel_traits`, this can be done as follows.
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\code
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template < class Point >
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@ -10,7 +10,7 @@ that satisfy the equation
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\f[ l:\; a\, x +b\, y +c = 0. \f]
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The line splits \f$ \E^2\f$ in a <I>positive</I> and a <I>negative</I>
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side. A point \f$ p\f$ with %Cartesian coordinates
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side. A point `p` with %Cartesian coordinates
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\f$ (px, py)\f$ is on the positive side of `l`, iff
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\f$ a\, px + b\, py +c > 0\f$, it is
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on the negative side of `l`, iff
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@ -28,7 +28,7 @@ the suffix `_2` and the representation type `Cartesian`.
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Point_2< Cartesian<double> > p(1.0,1.0), q(4.0,7.0);
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\endcode
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To define a line \f$ l\f$ we write:
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To define a line `l` we write:
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\code
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Line_2< Cartesian<double> > l(p,q);
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@ -51,31 +51,31 @@ coordinates \f$ ax +by +c = 0\f$.
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Line_2(const Kernel::RT &a, const Kernel::RT &b, const Kernel::RT &c);
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/*!
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introduces a line `l` passing through the points \f$ p\f$ and \f$ q\f$.
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Line `l` is directed from \f$ p\f$ to \f$ q\f$.
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introduces a line `l` passing through the points `p` and `q`.
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Line `l` is directed from `p` to `q`.
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*/
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Line_2(const Point_2<Kernel> &p, const Point_2<Kernel> &q);
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/*!
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introduces a line `l` passing through point \f$ p\f$ with
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direction \f$ d\f$.
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introduces a line `l` passing through point `p` with
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direction `d`.
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*/
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Line_2(const Point_2<Kernel> &p, const Direction_2<Kernel>&d);
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/*!
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introduces a line `l` passing through point \f$ p\f$ and
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oriented by \f$ v\f$.
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introduces a line `l` passing through point `p` and
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oriented by `v`.
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*/
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Line_2(const Point_2<Kernel> &p, const Vector_2<Kernel>&v);
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/*!
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introduces a line `l` supporting the segment \f$ s\f$,
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introduces a line `l` supporting the segment `s`,
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oriented from source to target.
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*/
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Line_2(const Segment_2<Kernel> &s);
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/*!
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introduces a line `l` supporting the ray \f$ r\f$,
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introduces a line `l` supporting the ray `r`,
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with same orientation.
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*/
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Line_2(const Ray_2<Kernel> &r);
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@ -97,17 +97,17 @@ Test for inequality.
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bool operator!=(const Line_2<Kernel> &h) const;
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/*!
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returns the first coefficient of \f$ l\f$.
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returns the first coefficient of `l`.
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*/
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Kernel::RT a() const;
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/*!
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returns the second coefficient of \f$ l\f$.
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returns the second coefficient of `l`.
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*/
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Kernel::RT b() const;
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/*!
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returns the third coefficient of \f$ l\f$.
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returns the third coefficient of `l`.
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*/
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Kernel::RT c() const;
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@ -120,7 +120,7 @@ to `point(j)`, for all `i` \f$ <\f$ `j`.
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Point_2<Kernel> point(int i) const;
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/*!
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returns the orthogonal projection of \f$ p\f$ onto `l`.
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returns the orthogonal projection of `p` onto `l`.
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*/
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Point_2<Kernel> projection(const Point_2<Kernel> &p) const;
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@ -163,7 +163,7 @@ bool is_vertical() const;
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returns \ref ON_ORIENTED_BOUNDARY,
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\ref ON_NEGATIVE_SIDE, or the constant
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\ref ON_POSITIVE_SIDE,
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depending on the position of \f$ p\f$ relative to the oriented line `l`.
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depending on the position of `p` relative to the oriented line `l`.
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*/
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Oriented_side oriented_side(const Point_2<Kernel> &p) const;
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@ -209,14 +209,14 @@ returns the line with opposite direction.
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Line_2<Kernel> opposite() const;
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/*!
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returns the line perpendicular to `l` and passing through \f$ p\f$,
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returns the line perpendicular to `l` and passing through `p`,
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where the direction is the direction of `l` rotated
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counterclockwise by 90 degrees.
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*/
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Line_2<Kernel> perpendicular(const Point_2<Kernel> &p) const;
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/*!
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returns the line obtained by applying \f$ t\f$ on a point on `l`
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returns the line obtained by applying `t` on a point on `l`
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and the direction of `l`.
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*/
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Line_2<Kernel> transform(const Aff_transformation_2<Kernel> &t) const;
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@ -17,31 +17,31 @@ public:
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/// @{
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/*!
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introduces a line `l` passing through the points \f$ p\f$ and \f$ q\f$.
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Line `l` is directed from \f$ p\f$ to \f$ q\f$.
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introduces a line `l` passing through the points `p` and `q`.
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Line `l` is directed from `p` to `q`.
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*/
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Line_3(const Point_3<Kernel> &p, const Point_3<Kernel> &q);
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/*!
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introduces a line `l` passing through point \f$ p\f$ with
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direction \f$ d\f$.
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introduces a line `l` passing through point `p` with
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direction `d`.
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*/
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Line_3(const Point_3<Kernel> &p, const Direction_3<Kernel>&d);
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/*!
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introduces a line `l` passing through point \f$ p\f$ and
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oriented by \f$ v\f$.
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introduces a line `l` passing through point `p` and
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oriented by `v`.
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*/
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Line_3(const Point_3<Kernel> &p, const Vector_3<Kernel>&v);
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/*!
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returns the line supporting the segment \f$ s\f$,
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returns the line supporting the segment `s`,
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oriented from source to target.
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*/
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Line_3(const Segment_3<Kernel> &s);
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/*!
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returns the line supporting the ray \f$ r\f$, with the
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returns the line supporting the ray `r`, with the
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same orientation.
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*/
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Line_3(const Ray_3<Kernel> &r);
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@ -63,7 +63,7 @@ Test for inequality.
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bool operator!=(const Line_3<Kernel> &h) const;
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/*!
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returns the orthogonal projection of \f$ p\f$ on `l`.
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returns the orthogonal projection of `p` on `l`.
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*/
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Point_3<Kernel> projection(const Point_3<Kernel> &p) const;
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@ -94,7 +94,7 @@ bool has_on(const Point_3<Kernel> &p) const;
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/// @{
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/*!
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returns the plane perpendicular to `l` passing through \f$ p\f$.
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returns the plane perpendicular to `l` passing through `p`.
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*/
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Plane_3<Kernel> perpendicular_plane(const Point_3<Kernel> &p) const;
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@ -114,7 +114,7 @@ returns the direction of `l`.
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Direction_3<Kernel> direction() const;
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/*!
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returns the line obtained by applying \f$ t\f$ on a point on `l`
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returns the line obtained by applying `t` on a point on `l`
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and the direction of `l`.
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*/
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Line_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;
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@ -10,7 +10,7 @@ the plane equation
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\f[h :\; a\, x +b\, y +c\, z + d = 0.\f]
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The plane splits \f$ \E^3\f$ in a <I>positive</I> and a <I>negative side</I>.
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A point \f$ p\f$ with %Cartesian coordinates \f$ (px, py, pz)\f$ is on the
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A point `p` with %Cartesian coordinates \f$ (px, py, pz)\f$ is on the
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positive side of `h`, iff \f$ a\, px +b\, py +c\, pz + d > 0\f$.
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It is on the negative side, iff \f$ a\, px +b\, py\, +c\, pz + d < 0\f$.
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@ -131,7 +131,7 @@ the negative to the positive side of `h`.
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Line_3<Kernel> perpendicular_line(const Point_3<Kernel> &p) const;
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/*!
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returns the orthogonal projection of \f$ p\f$ on `h`.
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returns the orthogonal projection of `p` on `h`.
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*/
|
||||
Point_3<Kernel> projection(const Point_3<Kernel> &p) const;
|
||||
|
||||
|
|
@ -187,7 +187,7 @@ under an affine transformation, which maps `h` onto the
|
|||
Point_2<Kernel> to_2d(const Point_3<Kernel> &p) const;
|
||||
|
||||
/*!
|
||||
returns a point \f$ q\f$, such that `to_2d( to_3d( p ))`
|
||||
returns a point `q`, such that `to_2d( to_3d( p ))`
|
||||
is equal to `p`.
|
||||
*/
|
||||
Point_3<Kernel> to_3d(const Point_2<Kernel> &p) const;
|
||||
|
|
@ -201,7 +201,7 @@ Point_3<Kernel> to_3d(const Point_2<Kernel> &p) const;
|
|||
returns either \ref ON_ORIENTED_BOUNDARY, or
|
||||
the constant \ref ON_POSITIVE_SIDE, or the constant
|
||||
\ref ON_NEGATIVE_SIDE,
|
||||
determined by the position of \f$ p\f$ relative to the oriented plane `h`.
|
||||
determined by the position of `p` relative to the oriented plane `h`.
|
||||
|
||||
*/
|
||||
Oriented_side oriented_side(const Point_3<Kernel> &p) const;
|
||||
|
|
@ -248,7 +248,7 @@ bool is_degenerate() const;
|
|||
/// @{
|
||||
|
||||
/*!
|
||||
returns the plane obtained by applying \f$ t\f$ on a point of `h`
|
||||
returns the plane obtained by applying `t` on a point of `h`
|
||||
and the orthogonal direction of `h`.
|
||||
*/
|
||||
Plane_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;
|
||||
|
|
|
|||
|
|
@ -185,7 +185,7 @@ are not parameterized with whatsoever.
|
|||
Bbox_2 bbox() const;
|
||||
|
||||
/*!
|
||||
returns the point obtained by applying \f$ t\f$ on `p`.
|
||||
returns the point obtained by applying `t` on `p`.
|
||||
*/
|
||||
Point_2<Kernel> transform(const Aff_transformation_2<Kernel> &t) const;
|
||||
|
||||
|
|
|
|||
|
|
@ -175,7 +175,7 @@ returns a bounding box containing `p`.
|
|||
Bbox_3 bbox() const;
|
||||
|
||||
/*!
|
||||
returns the point obtained by applying \f$ t\f$ on `p`.
|
||||
returns the point obtained by applying `t` on `p`.
|
||||
*/
|
||||
Point_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;
|
||||
|
||||
|
|
|
|||
|
|
@ -19,25 +19,25 @@ public:
|
|||
|
||||
/*!
|
||||
introduces a ray `r`
|
||||
with source \f$ p\f$ and passing through point \f$ q\f$.
|
||||
with source `p` and passing through point `q`.
|
||||
*/
|
||||
Ray_2(const Point_2<Kernel> &p, const Point_2<Kernel>&q);
|
||||
|
||||
/*!
|
||||
introduces a ray `r` starting at source \f$ p\f$ with
|
||||
direction \f$ d\f$.
|
||||
introduces a ray `r` starting at source `p` with
|
||||
direction `d`.
|
||||
*/
|
||||
Ray_2(const Point_2<Kernel> &p, const Direction_2<Kernel> &d);
|
||||
|
||||
/*!
|
||||
introduces a ray `r` starting at source \f$ p\f$ with
|
||||
the direction of \f$ v\f$.
|
||||
introduces a ray `r` starting at source `p` with
|
||||
the direction of `v`.
|
||||
*/
|
||||
Ray_2(const Point_2<Kernel> &p, const Vector_2<Kernel> &v);
|
||||
|
||||
/*!
|
||||
introduces a ray `r` starting at source \f$ p\f$ with
|
||||
the same direction as \f$ l\f$.
|
||||
introduces a ray `r` starting at source `p` with
|
||||
the same direction as `l`.
|
||||
*/
|
||||
Ray_2(const Point_2<Kernel> &p, const Line_2<Kernel> &l);
|
||||
|
||||
|
|
@ -117,10 +117,10 @@ of `r`, or if it is in the interior of `r`.
|
|||
bool has_on(const Point_2<Kernel> &p) const;
|
||||
|
||||
/*!
|
||||
checks if point \f$ p\f$ is on `r`. This function is faster
|
||||
checks if point `p` is on `r`. This function is faster
|
||||
than function `has_on()` if the precondition
|
||||
checking is disabled.
|
||||
\pre \f$ p\f$ is on the supporting line of `r`.
|
||||
\pre `p` is on the supporting line of `r`.
|
||||
*/
|
||||
bool collinear_has_on(const Point_2<Kernel> &p) const;
|
||||
|
||||
|
|
@ -130,7 +130,7 @@ bool collinear_has_on(const Point_2<Kernel> &p) const;
|
|||
/// @{
|
||||
|
||||
/*!
|
||||
returns the ray obtained by applying \f$ t\f$ on the source
|
||||
returns the ray obtained by applying `t` on the source
|
||||
and on the direction of `r`.
|
||||
*/
|
||||
Ray_2<Kernel> transform(const Aff_transformation_2<Kernel> &t) const;
|
||||
|
|
|
|||
|
|
@ -19,25 +19,25 @@ public:
|
|||
|
||||
/*!
|
||||
introduces a ray `r`
|
||||
with source \f$ p\f$ and passing through point \f$ q\f$.
|
||||
with source `p` and passing through point `q`.
|
||||
*/
|
||||
Ray_3(const Point_3<Kernel> &p, const Point_3<Kernel> &q);
|
||||
|
||||
/*!
|
||||
introduces a ray `r` with source \f$ p\f$ and with
|
||||
direction \f$ d\f$.
|
||||
introduces a ray `r` with source `p` and with
|
||||
direction `d`.
|
||||
*/
|
||||
Ray_3(const Point_3<Kernel> &p, const Direction_3<Kernel> &d);
|
||||
|
||||
/*!
|
||||
introduces a ray `r` with source \f$ p\f$ and with
|
||||
a direction given by \f$ v\f$.
|
||||
introduces a ray `r` with source `p` and with
|
||||
a direction given by `v`.
|
||||
*/
|
||||
Ray_3(const Point_3<Kernel> &p, const Vector_3<Kernel> &v);
|
||||
|
||||
/*!
|
||||
introduces a ray `r` starting at source \f$ p\f$ with
|
||||
the same direction as \f$ l\f$.
|
||||
introduces a ray `r` starting at source `p` with
|
||||
the same direction as `l`.
|
||||
*/
|
||||
Ray_3(const Point_3<Kernel> &p, const Line_3<Kernel> &l);
|
||||
|
||||
|
|
@ -102,7 +102,7 @@ of `r`, or if it is in the interior of `r`.
|
|||
bool has_on(const Point_3<Kernel> &p) const;
|
||||
|
||||
/*!
|
||||
returns the ray obtained by applying \f$ t\f$ on the source
|
||||
returns the ray obtained by applying `t` on the source
|
||||
and on the direction of `r`.
|
||||
*/
|
||||
Ray_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;
|
||||
|
|
|
|||
|
|
@ -7,9 +7,9 @@ An object `s` of the data type `Segment_2` is a directed
|
|||
straight line segment in the two-dimensional Euclidean plane \f$ \E^2\f$, i.e.\ a
|
||||
straight line segment \f$ [p,q]\f$ connecting two points \f$ p,q \in \R^2\f$.
|
||||
The segment is topologically closed, i.e.\ the end
|
||||
points belong to it. Point \f$ p\f$ is called the <I>source</I> and \f$ q\f$
|
||||
is called the <I>target</I> of \f$ s\f$. The length of \f$ s\f$ is the
|
||||
Euclidean distance between \f$ p\f$ and \f$ q\f$. Note that there is only a function
|
||||
points belong to it. Point `p` is called the <I>source</I> and `q`
|
||||
is called the <I>target</I> of `s`. The length of `s` is the
|
||||
Euclidean distance between `p` and `q`. Note that there is only a function
|
||||
to compute the square of the length, because otherwise we had to
|
||||
perform a square root operation which is not defined for all
|
||||
number types, which is expensive, and may not be exact.
|
||||
|
|
@ -25,8 +25,8 @@ public:
|
|||
/// @{
|
||||
|
||||
/*!
|
||||
introduces a segment `s` with source \f$ p\f$
|
||||
and target \f$ q\f$. The segment is directed from the source towards
|
||||
introduces a segment `s` with source `p`
|
||||
and target `q`. The segment is directed from the source towards
|
||||
the target.
|
||||
*/
|
||||
Segment_2(const Point_2<Kernel> &p, const Point_2<Kernel> &q);
|
||||
|
|
@ -106,7 +106,7 @@ returns a segment with source and target point interchanged.
|
|||
Segment_2<Kernel> opposite() const;
|
||||
|
||||
/*!
|
||||
returns the line \f$ l\f$ passing through `s`. Line \f$ l\f$ has the
|
||||
returns the line `l` passing through `s`. Line `l` has the
|
||||
same orientation as segment `s`.
|
||||
*/
|
||||
Line_2<Kernel> supporting_line() const;
|
||||
|
|
@ -138,9 +138,9 @@ of `s`, or if it is in the interior of `s`.
|
|||
bool has_on(const Point_2<Kernel> &p) const;
|
||||
|
||||
/*!
|
||||
checks if point \f$ p\f$ is on segment `s`. This function is faster
|
||||
checks if point `p` is on segment `s`. This function is faster
|
||||
than function `has_on()`.
|
||||
\pre \f$ p\f$ is on the supporting line of `s`.
|
||||
\pre `p` is on the supporting line of `s`.
|
||||
*/
|
||||
bool collinear_has_on(const Point_2<Kernel> &p) const;
|
||||
|
||||
|
|
@ -155,7 +155,7 @@ returns a bounding box containing `s`.
|
|||
Bbox_2 bbox() const;
|
||||
|
||||
/*!
|
||||
returns the segment obtained by applying \f$ t\f$ on the source
|
||||
returns the segment obtained by applying `t` on the source
|
||||
and the target of `s`.
|
||||
*/
|
||||
Segment_2<Kernel> transform(const Aff_transformation_2<Kernel> &t) const;
|
||||
|
|
|
|||
|
|
@ -3,13 +3,13 @@ namespace CGAL {
|
|||
/*!
|
||||
\ingroup kernel_classes3
|
||||
|
||||
An object \f$ s\f$ of the data type `Segment_3` is a directed
|
||||
An object `s` of the data type `Segment_3` is a directed
|
||||
straight line segment in the three-dimensional Euclidean space \f$ \E^3\f$,
|
||||
that is a straight line segment \f$ [p,q]\f$ connecting two points \f$ p,q \in
|
||||
\R^3\f$. The segment is topologically closed, i.e.\ the end
|
||||
points belong to it. Point \f$ p\f$ is called the <I>source</I> and \f$ q\f$
|
||||
is called the <I>target</I> of \f$ s\f$. The length of \f$ s\f$ is the
|
||||
Euclidean distance between \f$ p\f$ and \f$ q\f$. Note that there is only a function
|
||||
points belong to it. Point `p` is called the <I>source</I> and `q`
|
||||
is called the <I>target</I> of `s`. The length of `s` is the
|
||||
Euclidean distance between `p` and `q`. Note that there is only a function
|
||||
to compute the square of the length, because otherwise we had to
|
||||
perform a square root operation which is not defined for all
|
||||
number types, which is expensive, and may not be exact.
|
||||
|
|
@ -25,8 +25,8 @@ public:
|
|||
/// @{
|
||||
|
||||
/*!
|
||||
introduces a segment `s` with source \f$ p\f$
|
||||
and target \f$ q\f$. It is directed from the source towards
|
||||
introduces a segment `s` with source `p`
|
||||
and target `q`. It is directed from the source towards
|
||||
the target.
|
||||
*/
|
||||
Segment_3(const Point_3<Kernel> &p, const Point_3<Kernel> &q);
|
||||
|
|
@ -106,7 +106,7 @@ returns a segment with source and target interchanged.
|
|||
Segment_3<Kernel> opposite() const;
|
||||
|
||||
/*!
|
||||
returns the line \f$ l\f$ passing through `s`. Line \f$ l\f$ has the
|
||||
returns the line `l` passing through `s`. Line `l` has the
|
||||
same orientation as segment `s`, that is
|
||||
from the source to the target of `s`.
|
||||
*/
|
||||
|
|
@ -129,7 +129,7 @@ returns a bounding box containing `s`.
|
|||
Bbox_3 bbox() const;
|
||||
|
||||
/*!
|
||||
returns the segment obtained by applying \f$ t\f$ on the source
|
||||
returns the segment obtained by applying `t` on the source
|
||||
and the target of `s`.
|
||||
*/
|
||||
Segment_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;
|
||||
|
|
|
|||
|
|
@ -3,7 +3,7 @@ namespace CGAL {
|
|||
/*!
|
||||
\ingroup kernel_classes3
|
||||
|
||||
An object \f$ t\f$ of the class `Tetrahedron_3` is an oriented
|
||||
An object `t` of the class `Tetrahedron_3` is an oriented
|
||||
tetrahedron in the three-dimensional Euclidean space \f$ \E^3\f$.
|
||||
|
||||
It is defined by four vertices \f$ p_0\f$, \f$ p_1\f$, \f$ p_2\f$ and \f$ p_3\f$.
|
||||
|
|
|
|||
|
|
@ -3,9 +3,9 @@ namespace CGAL {
|
|||
/*!
|
||||
\ingroup kernel_classes2
|
||||
|
||||
An object \f$ t\f$ of the class `Triangle_2` is a triangle
|
||||
An object `t` of the class `Triangle_2` is a triangle
|
||||
in the two-dimensional Euclidean plane \f$ \E^2\f$.
|
||||
Triangle \f$ t\f$ is oriented, i.e., its boundary has
|
||||
Triangle `t` is oriented, i.e., its boundary has
|
||||
clockwise or counterclockwise orientation. We call the side to the left
|
||||
of the boundary the positive side and the side to the right of the
|
||||
boundary the negative side.
|
||||
|
|
@ -24,7 +24,7 @@ public:
|
|||
/// @{
|
||||
|
||||
/*!
|
||||
introduces a triangle `t` with vertices \f$ p\f$, \f$ q\f$ and \f$ r\f$.
|
||||
introduces a triangle `t` with vertices `p`, `q` and `r`.
|
||||
*/
|
||||
Triangle_2(const Point_2<Kernel> &p,
|
||||
const Point_2<Kernel> &q,
|
||||
|
|
@ -79,7 +79,7 @@ returns
|
|||
`POSITIVE_SIDE`,
|
||||
or the constant
|
||||
`ON_NEGATIVE_SIDE`,
|
||||
determined by the position of point \f$ p\f$.
|
||||
determined by the position of point `p`.
|
||||
\pre `t` is not degenerate.
|
||||
*/
|
||||
Oriented_side oriented_side(const Point_2<Kernel> &p) const;
|
||||
|
|
@ -88,7 +88,7 @@ Oriented_side oriented_side(const Point_2<Kernel> &p) const;
|
|||
returns the constant `ON_BOUNDARY`,
|
||||
`ON_BOUNDED_SIDE`, or else
|
||||
`ON_UNBOUNDED_SIDE`,
|
||||
depending on where point \f$ p\f$ is.
|
||||
depending on where point `p` is.
|
||||
\pre `t` is not degenerate.
|
||||
*/
|
||||
Bounded_side bounded_side(const Point_2<Kernel> &p) const;
|
||||
|
|
|
|||
|
|
@ -3,7 +3,7 @@ namespace CGAL {
|
|||
/*!
|
||||
\ingroup kernel_classes3
|
||||
|
||||
An object \f$ t\f$ of the class `Triangle_3` is a triangle in
|
||||
An object `t` of the class `Triangle_3` is a triangle in
|
||||
the three-dimensional Euclidean space \f$ \E^3\f$. As the triangle is not
|
||||
a full-dimensional object there is only a test whether a point lies on
|
||||
the triangle or not.
|
||||
|
|
@ -19,7 +19,7 @@ public:
|
|||
/// @{
|
||||
|
||||
/*!
|
||||
introduces a triangle `t` with vertices \f$ p\f$, \f$ q\f$ and \f$ r\f$.
|
||||
introduces a triangle `t` with vertices `p`, `q` and `r`.
|
||||
*/
|
||||
Triangle_3(const Point_3<Kernel> &p,
|
||||
const Point_3<Kernel> &q,
|
||||
|
|
|
|||
|
|
@ -44,12 +44,12 @@ introduces the vector \f$ s.target()-s.source()\f$.
|
|||
Vector_2(const Segment_2<Kernel> &s);
|
||||
|
||||
/*!
|
||||
introduces the vector having the same direction as \f$ r\f$.
|
||||
introduces the vector having the same direction as `r`.
|
||||
*/
|
||||
Vector_2(const Ray_2<Kernel> &r);
|
||||
|
||||
/*!
|
||||
introduces the vector having the same direction as \f$ l\f$.
|
||||
introduces the vector having the same direction as `l`.
|
||||
*/
|
||||
Vector_2(const Line_2<Kernel> &l);
|
||||
|
||||
|
|
@ -182,7 +182,7 @@ returns the direction which passes through `v`.
|
|||
Direction_2<Kernel> direction() const;
|
||||
|
||||
/*!
|
||||
returns the vector obtained by applying \f$ t\f$ on `v`.
|
||||
returns the vector obtained by applying `t` on `v`.
|
||||
*/
|
||||
Vector_2<Kernel> transform(const Aff_transformation_2<Kernel> &t) const;
|
||||
|
||||
|
|
|
|||
|
|
@ -46,12 +46,12 @@ introduces the vector \f$ s.target()-s.source()\f$.
|
|||
Vector_3(const Segment_3<Kernel> &s);
|
||||
|
||||
/*!
|
||||
introduces a vector having the same direction as \f$ r\f$.
|
||||
introduces a vector having the same direction as `r`.
|
||||
*/
|
||||
Vector_3(const Ray_3<Kernel> &r);
|
||||
|
||||
/*!
|
||||
introduces a vector having the same direction as \f$ l\f$.
|
||||
introduces a vector having the same direction as `l`.
|
||||
*/
|
||||
Vector_3(const Line_3<Kernel> &l);
|
||||
|
||||
|
|
@ -187,7 +187,7 @@ returns the dimension (the constant 3).
|
|||
int dimension() const;
|
||||
|
||||
/*!
|
||||
returns the vector obtained by applying \f$ t\f$ on `v`.
|
||||
returns the vector obtained by applying `t` on `v`.
|
||||
*/
|
||||
Vector_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue